Geometry

Question Analysis:
This question involves classifying a quadrilateral using its vertices on the coordinate plane.
The main focus is on verifying whether the figure is a rectangle by checking:
All angles are right angles (i.e., adjacent sides are perpendicular) using the slope formula.
Also confirm opposite sides are equal using the distance formula.

Key Concept Explanation:
A rectangle is a quadrilateral where:
Opposite sides are equal in length.
Adjacent sides are perpendicular, forming four right angles.
So, we’ll use:
Slope formula to check for perpendicularity:
If the product of two adjacent slopes is −1, they’re perpendicular.
Distance formula to verify opposite sides are equal.

Step-by-Step Solution:
Compute Slopes of All Sides
WX: (1 − 1) / (6 − 2) = 0 / 4 = 0
XY: (4 − 1) / (6 − 6) = 3 / 0 → undefined
→ WX ⟂ XY ✔
YZ: (4 − 4) / (2 − 6) = 0 / (−4) = 0
ZW: (1 − 4) / (2 − 2) = (−3) / 0 → undefined
→ YZ ⟂ ZW ✔
→ All adjacent sides are perpendicular ⇒ All angles are 90° ✔
Compute Side Lengths Using Distance Formula
WX = √[(6−2)² + (1−1)²] = √[16 + 0] = √16 = 4
XY = √[(6−6)² + (4−1)²] = √[0 + 9] = √9 = 3
YZ = √[(6−2)² + (4−4)²] = √[16 + 0] = √16 = 4
ZW = √[(2...